The Journal of the Indian Mathematical Society

G. Sankaranarayanan ¹

Affiliations
1 Annamalai University, Annamalai Nagar, IN

Abstract

Consider the process of events consisting in the arrival of particles to a counter. Let each particle arriving in the time interval (0,∞) independently of others give rise to an impulse with probability one.

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G. Sankaranarayanan ¹

Affiliations
1 Annamalai University, Annamalainagar, IN

Abstract

Let (Q, F) be a measurable space and (1.1) P(x, E; t) = Pr[X(t+s) ∈ E/X(s)=x], x ∈Ω, E ∈ F, t > 0, be the transition probability for a Markoff Process X(t), t > 0, X(0)=x₀ with values in Ω. P(x, E; t) is a measure over F for fixed x, t and for each E is a measurable function in (x, t).

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G. Sankaranarayanan ¹

Affiliations
1 Annamalai University, IN

Abstract

Let X₁, X₂, ... be a sequence of independent real-valued random variables with a common distribution function F(x) = Pr(X_n ≤ x). Let S_n = X₁ + ... + X_n.

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