@@ -63,7 +63,7 @@ A **Kesten process** is a stochastic process of the form
6363 x_{t+1 } = a_{t+1 } x_t + \eta _{t+1 }
6464 \quad \text {with } x_0 \text { given}
6565
66- where :math: `\{ a_t\} _{t \geq 1 }` and :math: `\{\eta _t\} _{t \geq 1 }` are iid
66+ where :math: `\{ a_t\} _{t \geq 1 }` and :math: `\{\eta _t\} _{t \geq 1 }` are IID
6767sequences.
6868
6969We will focus on the nonnegative scalar case, where :math: `x_t` takes values
@@ -73,9 +73,9 @@ In particular, we will assume that
7373
7474* the initial condition :math: `x_0 ` is nonnegative,
7575
76- * :math: `\{ a_t\} _{t \geq 1 }` is a nonnegative iid stochastic process and
76+ * :math: `\{ a_t\} _{t \geq 1 }` is a nonnegative IID stochastic process and
7777
78- * :math: `\{\eta _t\} _{t \geq 1 }` is another nonnegative iid stochastic process, independent of the first.
78+ * :math: `\{\eta _t\} _{t \geq 1 }` is another nonnegative IID stochastic process, independent of the first.
7979
8080
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@@ -122,7 +122,7 @@ The GARCH(1, 1) volatility process takes the form
122122
123123 \sigma _{t+1 }^2 = \alpha _0 + \sigma _t^2 (\alpha _1 \xi _{t+1 }^2 + \beta )
124124
125- where :math: `\{\xi _t\}` is iid with :math: `\mathbb E \xi _t^2 = 1 ` and all parameters are positive.
125+ where :math: `\{\xi _t\}` is IID with :math: `\mathbb E \xi _t^2 = 1 ` and all parameters are positive.
126126
127127Returns on a given asset are then modeled as
128128
@@ -131,7 +131,7 @@ Returns on a given asset are then modeled as
131131
132132 r_t = \sigma _t \zeta _{t+1 }
133133
134- where :math: `\{\zeta _t\}` is again iid and independent of :math: `\{\xi _t\}`.
134+ where :math: `\{\zeta _t\}` is again IID and independent of :math: `\{\xi _t\}`.
135135
136136Notice that the volatility sequence :math: `\{\sigma _t\}`, which drives the dynamics, is a Kesten process.
137137
@@ -152,7 +152,7 @@ Wealth then evolves according to
152152
153153 where :math: `\{ R_t\}` is the gross rate of return on assets.
154154
155- If :math: `\{ R_t\}` and :math: `\{ y_t\}` are both iid , then :eq: `wealth_dynam `
155+ If :math: `\{ R_t\}` and :math: `\{ y_t\}` are both IID , then :eq: `wealth_dynam `
156156is a Kesten process.
157157
158158
@@ -386,7 +386,7 @@ We can express this idea by stating that a suitably defined measure
386386
387387 \frac {s_{t+1 }}{s_t} = a_{t+1 }
388388
389- for some positive iid sequence :math: `\{ a_t\}`.
389+ for some positive IID sequence :math: `\{ a_t\}`.
390390
391391One implication of Gibrat's law is that the growth rate of individual firms
392392does not depend on their size.
413413 s_{t+1 } = a_{t+1 } s_t + b_{t+1 }
414414
415415
416- where :math: `\{ a_t\}` and :math: `\{ b_t\}` are both iid and independent of each
416+ where :math: `\{ a_t\}` and :math: `\{ b_t\}` are both IID and independent of each
417417other.
418418
419419In the exercises you are asked to show that :eq: `firm_dynam ` is more
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