scholarly journals Additive functionals of the Brownian path

1961 ◽  
Vol 33 (3) ◽  
pp. 479-506 ◽  
Author(s):  
H. P. Jr. McKean ◽  
Hiroshi Tanaka
Keyword(s):  
Brownian Path ◽  
Additive Functionals

scholarly journals Additive functionals of the Brownian path

2002 ◽  
pp. 19-46
Author(s):  
H. P. MCKEAN ◽  
Hiroshi TANAKA
Keyword(s):  
Brownian Path ◽  
Additive Functionals

Note on Continuous Additive Functionals of the 1-Dimensional Brownian Path

2002 ◽  
pp. 47-53
Author(s):  
HIROSHI TANAKA
Keyword(s):  
Brownian Path ◽  
Additive Functionals

Limit distribution of additive functionals of diffusion processes

1968 ◽  
Vol 4 (5) ◽  
pp. 850-856
Author(s):  
R. Z. Khas'minskii
Keyword(s):  
Limit Distribution ◽  
Diffusion Processes ◽  
Additive Functionals

scholarly journals A Limit Theorem for Nonnegative Additive Functionals of Storage Processes

1985 ◽  
Vol 13 (2) ◽  
pp. 397-413 ◽  
Author(s):  
Keigo Yamada
Keyword(s):  
Limit Theorem ◽  
Additive Functionals ◽  
Storage Processes

scholarly journals A Malliavin Calculus method to study densities of additive functionals of SDE’s with irregular drifts

2012 ◽  
Vol 48 (3) ◽  
pp. 871-883 ◽  
Author(s):  
Arturo Kohatsu-Higa ◽  
Akihiro Tanaka
Keyword(s):  
Malliavin Calculus ◽  
Additive Functionals

ON the Openness of Functors of k-Nonexpanding and Weakly Additive Functionals

2014 ◽  
Vol 65 (11) ◽  
pp. 1733-1742
Author(s):  
L. I. Karchevs’ka
Keyword(s):  
Additive Functionals

scholarly journals Representation of additive functionals on vector-valued normed Köthe spaces

1979 ◽  
Vol 2 (3) ◽  
pp. 300-313 ◽  
Author(s):  
Fumio Hiai
Keyword(s):  
Additive Functionals ◽  
Köthe Spaces ◽  
Vector Valued

Large deviations of generalized renewal process

2020 ◽  
Vol 30 (4) ◽  
pp. 215-241
Author(s):  
Gavriil A. Bakay ◽  
Aleksandr V. Shklyaev
Keyword(s):  
Large Deviations ◽  
Renewal Process ◽  
Limit Theorems ◽  
Local Limit ◽  
Asymptotic Formulas ◽  
Additive Functionals ◽  
Wide Range ◽  
Finite Markov Chains ◽  
Independent Identically Distributed ◽  
Local Limit Theorems

AbstractLet (ξ(i), η(i)) ∈ ℝd+1, 1 ≤ i < ∞, be independent identically distributed random vectors, η(i) be nonnegative random variables, the vector (ξ(1), η(1)) satisfy the Cramer condition. On the base of renewal process, NT = max{k : η(1) + … + η(k) ≤ T} we define the generalized renewal process ZT = $\begin{array}{} \sum_{i=1}^{N_T} \end{array}$ξ(i). Put IΔT(x) = {y ∈ ℝd : xj ≤ yj < xj + ΔT, j = 1, …, d}. We find asymptotic formulas for the probabilities P(ZT ∈ IΔT(x)) as ΔT → 0 and P(ZT = x) in non-lattice and arithmetic cases, respectively, in a wide range of x values, including normal, moderate, and large deviations. The analogous results were obtained for a process with delay in which the distribution of (ξ(1), η(1)) differs from the distribution on the other steps. Using these results, we prove local limit theorems for processes with regeneration and for additive functionals of finite Markov chains, including normal, moderate, and large deviations.

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

Densities for stationary random sets and point processes

1984 ◽  
Vol 16 (02) ◽  
pp. 324-346 ◽  
Author(s):  
Wolfgang Weil ◽  
John A. Wieacker
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Convex Set ◽  
Compact Convex ◽  
Random Sets ◽  
Intensity Measure ◽  
Additive Functionals ◽  
Compact Convex Set ◽  
Classical Integral

For certain stationary random setsX, densitiesDφ(X) of additive functionalsφare defined and formulas forare derived whenKis a compact convex set in. In particular, for the quermassintegrals and motioninvariantX, these formulas are in analogy with classical integral geometric formulas. The case whereXis the union set of a Poisson processYof convex particles is considered separately. Here, formulas involving the intensity measure ofYare obtained.

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