scholarly journals On the local time process of a skew Brownian motion

2019 ◽  
Vol 372 (5) ◽  
pp. 3597-3618 ◽  
Author(s):  
Andrei Borodin ◽  
Paavo Salminen
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Time Process ◽  
Skew Brownian Motion

Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time

2013 ◽  
Vol 50 (02) ◽  
pp. 592-597 ◽  
Author(s):  
Yaozhong Hu ◽  
Chihoon Lee
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Service Rate ◽  
Time Process ◽  
State Process ◽  
Drift Parameter

We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long-range dependent and self-similar input processes, where the drift parameter carries the physical meaning of the surplus service rate and plays a central role in the heavy-traffic approximation theory for queueing systems. We study a statistical estimator based on the cumulative local time process and establish its strong consistency and asymptotic normality.

scholarly journals Local time flow related to skew brownian motion

2001 ◽  
Vol 29 (4) ◽  
pp. 1693-1715 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Krzysztof Burdzy
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Skew Brownian Motion ◽  
Time Flow

scholarly journals Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time

2013 ◽  
Vol 50 (2) ◽  
pp. 592-597 ◽  
Author(s):  
Yaozhong Hu ◽  
Chihoon Lee
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Service Rate ◽  
Time Process ◽  
State Process ◽  
Drift Parameter

We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long-range dependent and self-similar input processes, where the drift parameter carries the physical meaning of the surplus service rate and plays a central role in the heavy-traffic approximation theory for queueing systems. We study a statistical estimator based on the cumulative local time process and establish its strong consistency and asymptotic normality.

scholarly journals Some limit theorems connected with Brownian local time

2006 ◽  
Vol 2006 ◽  
pp. 1-5
Author(s):  
Raouf Ghomrasni
Keyword(s):  
Brownian Motion ◽  
Large Class ◽  
Local Time ◽  
Limit Theorems ◽  
Standard Brownian Motion ◽  
Time Process ◽  
Continuous Version ◽  
Brownian Local Time ◽  
Class Of Functions

Let B=(Bt)t≥0 be a standard Brownian motion and let (Ltx;t≥0,x∈ℝ) be a continuous version of its local time process. We show that the following limitlim⁡ε↓0(1/2ε)∫0t{F(s,Bs−ε)−F(s,Bs+ε)}ds is well defined for a large class of functions F(t,x), and moreover we connect it with the integration with respect to local time Ltx . We give an illustrative example of the nonlinearity of the integration with respect to local time in the random case.

scholarly journals Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise

2021 ◽  
Author(s):  
David Baños ◽  
Salvador Ortiz-Latorre ◽  
Andrey Pilipenko ◽  
Frank Proske
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Solution Process ◽  
Variational Calculus ◽  
Strong Solutions ◽  
Skew Brownian Motion ◽  
Unknown Solution

AbstractIn this paper, we prove the existence of strong solutions to an stochastic differential equation with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters $$H<\frac{1}{2}.$$ H < 1 2 . Here, the generalized drift is given as the local time of the unknown solution process, which can be considered an extension of the concept of a skew Brownian motion to the case of fractional Brownian motion. Our approach for the construction of strong solutions is new and relies on techniques from Malliavin calculus combined with a “local time variational calculus” argument.

Self-avoiding random walk: A Brownian motion model with local time drift

1987 ◽  
Vol 74 (2) ◽  
pp. 271-287 ◽  
Author(s):  
J. R. Norris ◽  
L. C. G. Rogers ◽  
David Williams
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Motion Model ◽  
Time Drift ◽  
Brownian Motion Model
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