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In this paper, we introduce the linear self-attracting diffusion driven by a weighted fractional Brownian motion with weighting exponent $a>-1$ and Hurst index $|b|<a+1,0<b<1$, which is analogous to the linear fractional self-attracting diffusion. For the 1-dimensional process we study its convergence and the corresponding weighted local time. As a related problem, we also obtain the renormalized intersection local time exists in $L^2$ if $\text{max}\{a_1+b_1,a_2+b_2\}<0$.
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참고문헌 (30)
참고문헌 신청
E. Alos / 2001 / Stochastic calculus with respect to Gaussian processes / Ann. Probab 29(2):766~801
Simeon Berman / 1973 / Local nondeterminism and local times of Gaussian processes / Indiana University Mathematics Journal 23(1):69~94
Tomasz Bojdecki / 2007 / Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems / Electronic Communications in Probability 12:161~172
T. Bojdecki / 2008 / Occupation time limits of inhomogeneous Poisson systems of independent particles / Stochastic Processes and their Applications 118(1):28~52
Tomasz Bojdecki / 2008 / Self-Similar Stable Processes Arising from High-Density Limits of Occupation Times of Particle Systems / Potential Analysis 28(1):71~103
Simeon Berman / 1973 / Local nondeterminism and local times of Gaussian processes / Indiana University Mathematics Journal 23(1):69~94
Tomasz Bojdecki / 2007 / Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems / Electronic Communications in Probability 12:161~172
T. Bojdecki / 2008 / Occupation time limits of inhomogeneous Poisson systems of independent particles / Stochastic Processes and their Applications 118(1):28~52
Tomasz Bojdecki / 2008 / Self-Similar Stable Processes Arising from High-Density Limits of Occupation Times of Particle Systems / Potential Analysis 28(1):71~103
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