Exact Simulation of Brownian Diffusions with Drift Admitting Jumps
نویسندگان
چکیده
In this paper, using an algorithm based on retrospective rejection sampling scheme introduced in [2, 6], we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical difficulty due to the presence of two jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.
منابع مشابه
Asymptotic properties of certain diffusion ratchets with locally negative drift
We consider two reflecting diffusion processes (Xt)t≥0 with a moving reflection boundary given by a non-decreasing pure jump Markov process (Rt)t≥0. Between the jumps of the reflection boundary the diffusion part behaves as a reflecting Brownian motion with negative drift or as a reflecting Ornstein-Uhlenbeck process. In both cases at rate γ(Xt − Rt) for some γ ≥ 0 the reflection boundary jumps...
متن کاملOn Product-form Stationary Distributions for Reflected Diffusions with Jumps in the Positive Orthant
In this paper we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R+ that satisfies certain finiteness conditions, we characterize the Fokker-Planck equation. We then provide necessary and sufficient conditions for the existence of a product-form distribution for diffusion...
متن کاملEstimating functions for jump-diffusions
The theory of approximate martingale estimating functions for continuous diffusions is well developed and encompasses many estimators proposed in the literature. This paper extends the asymptotic theory for approximate martingale estimating functions to diffusions with finite-activity jumps. The primary aim is to shed light on the question of rate optimality and efficiency of estimators when ob...
متن کاملExact simulation of the Wright-Fisher diffusion
The Wright-Fisher family of diffusion processes is a class of evolutionary models widely used in population genetics, with applications also in finance and Bayesian statistics. Simulation and inference from these diffusions is therefore of widespread interest. However, simulating a Wright-Fisher diffusion is difficult because there is no known closed-form formula for its transition function. In...
متن کاملThe Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions
The main objective of this paper is to explore the relationship between the stochastic maximum principle (SMP in short) and dynamic programming principle (DPP in short), for singular control problems of jump diffusions. First, we establish necessary as well as sufficient conditions for optimality by using the stochastic calculus of jump diffusions and some properties of singular controls. Then,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Scientific Computing
دوره 39 شماره
صفحات -
تاریخ انتشار 2017