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The separation method is used obtain sufficient conditions for the solvability of the main (according to Galiullin’s classification) inverse problem in the class of first-order It? stochastic differential systems with random pert...
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The separation method is used obtain sufficient conditions for the solvability of the main (according to Galiullin’s classification) inverse problem in the class of first-order It? stochastic differential systems with random perturbations from the class of Wiener processes and diffusion degenerate with respect to a part of variables.
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Motivated by our earlier work on change-point analysis we prove a number of limit theorems for increments of renewal counting processes, or the corresponding first passage times. The starting point of the increments is determinist...
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Motivated by our earlier work on change-point analysis we prove a number of limit theorems for increments of renewal counting processes, or the corresponding first passage times. The starting point of the increments is deterministic as well as random, a typical example being the first stopping time to detect a change-point of some (continuously) observed process.
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It is well-known that the Skorohod reflection of a Wiener process is the absolute value of another Wiener process with finer filtration. In other words it can be unfolded to obtain a Wiener process. In this short note a similar st...
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It is well-known that the Skorohod reflection of a Wiener process is the absolute value of another Wiener process with finer filtration. In other words it can be unfolded to obtain a Wiener process. In this short note a similar statement is proved for continuous semimartingales.
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Head wear becomes inevitable as the physical clearance between the head and disk in current hard disk drives is close to 1 nm or lower. Accurate characterization of the wear process is essential in understanding the wear mechanism...
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Head wear becomes inevitable as the physical clearance between the head and disk in current hard disk drives is close to 1 nm or lower. Accurate characterization of the wear process is essential in understanding the wear mechanism, evaluating the reliability of hard disk drives (HDDs), and predicting the future evolution of wear as well as guiding the design of HDDs of later vintages. Due to the variations in the material and geometry of magnetic head, the wear process is dynamic and stochastic. To cope with the dynamics, a Wiener process with a positive drift is used to model the wear process. Furthermore, to evaluate the reliability quickly, an accelerated degradation model using the wear measurements is developed, from which the parameters/failure times under light loads can be effectively predicted. The developed model is then applied to a real wear problem of magnetic head to demonstrate the effectiveness.
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S. Orey and S. J. Taylor (1974, Proc. London Math. Soc. 28, 174-192) proved that for 0 ≤ λ ≤ 1 the set E(λ) = {t ∈ [0, 1] : lim sup_(h↓0)(2h log (1/h))~(-1/2)(W'(t + h)- W'(t)) ≥ λ} has Hausdorff dimension dim E(λ) = 1 - ...
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S. Orey and S. J. Taylor (1974, Proc. London Math. Soc. 28, 174-192) proved that for 0 ≤ λ ≤ 1 the set E(λ) = {t ∈ [0, 1] : lim sup_(h↓0)(2h log (1/h))~(-1/2)(W'(t + h)- W'(t)) ≥ λ} has Hausdorff dimension dim E(λ) = 1 - λ~2 a.s. where W'(t) is a standard Wiener process. A corresponding result is obtained when W' is replaced by a two-parameter Wiener process.
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Let {X,X_i; i ≥ 1} be a sequence of i.i.d.r.v'.s, Z(t) = ∑_(i=1)~t X_i, t ≥ 0. Consider the renewal process N(t) = inf{x; Z(x) > t}. In this paper we study the necessary moment conditions for {N(t);t ≥ 0} approximating to Wien...
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Let {X,X_i; i ≥ 1} be a sequence of i.i.d.r.v'.s, Z(t) = ∑_(i=1)~t X_i, t ≥ 0. Consider the renewal process N(t) = inf{x; Z(x) > t}. In this paper we study the necessary moment conditions for {N(t);t ≥ 0} approximating to Wiener processes. Our results have improved those of Csoergoe, Horvath and Steinebach.
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We prove the Wiener–Hopf factorization for Markov additive processes. We derive also Spitzer–Rogozin theorem for this class of processes which serves for obtaining Kendall’s formula and Fristedt representation of the cumulant m...
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We prove the Wiener–Hopf factorization for Markov additive processes. We derive also Spitzer–Rogozin theorem for this class of processes which serves for obtaining Kendall’s formula and Fristedt representation of the cumulant matrix of the ladder epoch process. Finally, we also obtain the so-called ballot theorem.
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Miller & Orr (1966, Q. J. Econ., 80, 413-435) formulate a cash management model under which an organization's cash flow evolves in terms of a stationary random walk. This, in turn, implies that the organization's demand for cash will not grow over time. However, as organizations grow one would expect the demand for cash to grow as well. Given this, we formulate a cash management model under which movements in an organization's cash balance hinge on its current rate of output or an equivalent size measure. Cash is withdrawn and invested in interest-bearing securities when the cash to output ratio becomes too high, while securities are sold and the proceeds deposited in a non-interest-bearing bank account when the cash to output ratio becomes too low. The control limits are determined so as to minimize the expected annual cost of a unit of output. Our analysis shows that when organization's cash flows follow a non-stationary process, the optimal cash management policies are profoundly different to those obtained under the Miller & Orr (1966) model....
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Miller & Orr (1966, Q. J. Econ., 80, 413-435) formulate a cash management model under which an organization's cash flow evolves in terms of a stationary random walk. This, in turn, implies that the organization's demand for cash will not grow over time. However, as organizations grow one would expect the demand for cash to grow as well. Given this, we formulate a cash management model under which movements in an organization's cash balance hinge on its current rate of output or an equivalent size measure. Cash is withdrawn and invested in interest-bearing securities when the cash to output ratio becomes too high, while securities are sold and the proceeds deposited in a non-interest-bearing bank account when the cash to output ratio becomes too low. The control limits are determined so as to minimize the expected annual cost of a unit of output. Our analysis shows that when organization's cash flows follow a non-stationary process, the optimal cash management policies are profoundly different to those obtained under the Miller & Orr (1966) model.
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Durbin (1992) derived a convergent series for the density of the first passage time of a Weiner process to a curved boundary. We show that the successive partial sums of this series can be expressed as the iterates of the standard...
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Durbin (1992) derived a convergent series for the density of the first passage time of a Weiner process to a curved boundary. We show that the successive partial sums of this series can be expressed as the iterates of the standard substitution method for solving an integral equation. The calculation is thus simpler than it first appears. We also show that, under a certain condition, the series converges uniformly. This strengthens Durbin's result of pointwise convergence. Finally, we present a modified procedure, based on scaling, which sometimes works better. These approaches cover some cases that Durbin did not.
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