Keigo Yamada

Explicit formula of optimal replacement under additive shock processes

The optimal machine replacement problem is discussed for the case, where damage processes are general jump processes. Considering an expected average cost and an expected discounted cost, an explicit formula of optimal replacement time is shown under appropriate conditions for damage processes.

A stability theorem for stochastic differential equations with application to storage processes, random walks and optimal stochastic control problems

For a sequence of stochastic differential equations of type Xn(t)=Xn(0)+[small esh]t0aN(S, XN(S-)) dAn(S)+[small esh]t0[small esh]R\{0}cn(S,Xn(S-))dn(S,Xn(S-),x)Nn(ds dx)+Bn(t), a stability theorem is presented under an appropriate convergence mode of coefficients an, cn, dn, driving processes An, Bn and martingale measures Nn. Applications to limit theorems for storage processes, random walks and optimal control problems are shown.

A stability theorem for stochastic differential equations and application to stochastic control problems

For a sequence of stochastic differential equations of the the type: a stabilty theorem is presented under appropritate convergence mode of [d] and m application to stochastic control problems is also briefly discussed.

Stability theorem for stochastic differential equations with jumps

Convergence in law of solutions of SDE having jumps is discussed assuming suitable convergence of the coefficients under a situation where the point process approaches a Poisson point process. As an application the asymptotic behavior of certain stochastic processes such as storage processes and random walks is also discussed.

Multi-dimensional Bessel processes as heavy traffic limits of certain tandem queues

For a sequence of multi-dimensional birth and death processes representing tandem queue models, it is shown that suitably normalized processes converge weakly to a certain type of multi-dimensional Bessel diffusions which are characterized as continuous semimartingales satisfying Skorohod type equations.

A bound for the expected hitting time of storage processes

An upper bound for the expected hitting time to a critical level is given for a storage process that can be described as a solution of a stochastic integral equation in which the input process is a jump process. This upper bound is applicable when suitable conditions hold for the local description of the jump process and for the parameters appearing in the storage equation.

Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes

We consider a class of storage models with finite or infinite capacities where input processes are pure jump processes having state-dependent Leavy measures. Conditions under which such storage models are approximated by reflecting or sticky diffusions or more generally Markov processes with Levy generators having nondegenerate diffusion coefficients are given.

Some exponential type bounds for hitting time distributions of storage processes

We consider a storage process with finite or infinite capacity having a compound Poisson process as input and general release rule. For this process we derive some exponential type upper and lower bounds for hitting time distributions by means of martingale theory.

Diffusion approximation for storage processes

For a sequence of storage processes with general release rate functions which contain, as a special case, queuing processes, we show that under appropriate conditions, suitably normalized processes for storage processes converge to diffusions in the sense of law.