This paper explores qualitative effects of lead-time uncertainty in a basic continuous-time single-item inventory model with Poisson demand and stochastic lead times. The objective is to minimize the infinite-horizon expected total discounted cost. Order costs are linear, so a base-stock policy is optimal. Traditionally and intuitively, people believe that a (stochastically) longer lead time re...

Abstract. In this paper we study the pathwise stochastic Taylor expansion, in the sense of our previous work [3], for a class of Itô-type random fields in which the di↵usion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an “self-exciting” type particularly contains the fully nonlinear stochastic PDEs of curvature driven di↵usion, as w...

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version ...

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version ...

The emergence of corona virus (COVID-19) has create a great public concern as the outbreak is still ongoing and government are taking actions such as holiday extension, travel restriction, temporary closure of public work place, borders, schools, quarantine/isolation, social distancing and so on. To mitigate the spread, we proposed and analyzed a stochastic model for the continue spread of coro...

Adaptive time-stepping methods based on the Monte Carlo Euler method for weak approximation of Itô stochastic differential equations are developed. The main result is new expansions of the computational error, with computable leading-order term in a posteriori form, based on stochastic flows and discrete dual backward problems. The expansions lead to efficient and accurate computation of error ...